In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A 2 R mk , B 2 R mp , m p k, we seek the minimum of kA?BQk 2 for all matrices Q 2 R pk , Q T Q = I kk. We introduce a class of relaxation methods for generating minimizing sequences and ooer a geometric interpretation of these methods. Results of numerical experiments illustrating the convergence of the methods are given.